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Style fixes for ellipj.cc, ellipke.m, and expint.m * ellipj.cc, ellipke.m, expint.m: Style fixes.
author Mike Miller <mtmiller@ieee.org>
date Sun, 28 Apr 2013 18:50:51 -0400
parents 1a3bfb14b5da
children a3fdd6041e64
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1 ## Copyright (C) 2006 Sylvain Pelissier <sylvain.pelissier@gmail.com>
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or (at
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8 ## your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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13 ## General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {} expint (@var{x})
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21 ## Compute the exponential integral,
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22 ## @verbatim
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23 ## infinity
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24 ## /
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25 ## expint(x) = | exp(t)/t dt
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26 ## /
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27 ## x
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28 ## @end verbatim
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29 ## @end deftypefn
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30
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31 function y = expint (x)
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32
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33 if (nargin != 1)
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34 print_usage ();
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35 endif
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36
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37 y = expint_E1 (x);
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38
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39 endfunction
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40
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41 ## -*- texinfo -*-
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42 ## @deftypefn {Function File} {@var{y} =} expint_E1 (@var{x})
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43 ## Compute the exponential integral,
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44 ## @verbatim
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45 ## infinity
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46 ## /
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47 ## expint(x) = | exp(t)/t dt
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48 ## /
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49 ## x
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50 ## @end verbatim
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51 ## @end deftypefn
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52
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53 function y = expint_E1 (x)
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54
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55 if (nargin != 1)
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56 print_usage ();
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57 endif
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58
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59 y = x;
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60
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61 idx = (imag (x) > 0 & imag (x) != 0);
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62 y(idx) = -expint_Ei (-y(idx)) - i.*pi;
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63
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64 idx = (imag (x) < 0 & imag (x) != 0);
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65 y(idx) = -expint_Ei (-y(idx)) + i.*pi;
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66
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67 idx = (real (x) >= 0 & imag (x) == 0);
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68 y(idx) = -expint_Ei (-y(idx));
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69
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70 idx = (real (x) < 0 & imag (x) == 0);
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71 y(idx) = -expint_Ei (-y(idx)) - i.*pi;
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72
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73 endfunction
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74
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75 ## -*- texinfo -*-
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76 ## @deftypefn {Function File} {@var{y} =} expint_Ei (@var{x})
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77 ## Compute the exponential integral,
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78 ## @verbatim
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79 ## infinity
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80 ## /
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81 ## expint_Ei(x) = - | exp(t)/t dt
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82 ## /
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83 ## -x
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84 ## @end verbatim
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85 ## @end deftypefn
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86
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87 function y = expint_Ei (x)
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88
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89 if (nargin != 1)
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90 print_usage ();
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91 endif
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92
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93 y = zeros (size (x));
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94 F = @(x) exp (-x)./x;
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95 s = prod (size (x));
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96
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97 for t = 1:s;
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98 if (x(t) < 0 && imag (x(t)) == 0)
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99 y(t) = -quad (F, -x(t), Inf);
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100 else
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101 if (abs (x(t)) > 2 && imag (x(t)) == 0)
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102 y(t) = expint_Ei (2) - quad (F, -x(t), -2);
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103 else
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104 if (abs (x(t)) >= 10)
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105 if (imag (x(t)) <= 0)
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106 a1 = 4.03640;
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107 a2 = 1.15198;
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108 b1 = 5.03637;
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109 b2 = 4.19160;
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110 y(t) = -(x(t).^2 - a1.*x(t) + a2) ...
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111 ./ ((x(t).^2 - b1.*x(t) + b2) .* (-x(t)) .* exp (-x(t))) ...
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112 - i.*pi;
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113 else
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114 y(t) = conj (expint_Ei (conj (x(t))));
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115 endif;
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116 ## Serie Expansion
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117 else
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118 for k = 1:100;
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119 y(t) = y(t) + x(t).^k ./ (k.*factorial (k));
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120 endfor
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121 y(t) = 0.577215664901532860606512090082402431 + log (x(t)) + y(t);
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122 endif
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123 endif
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124 endif
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125 endfor
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126 endfunction
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127
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128 %% Test against A&S Table 5.1
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129 %!test
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
130 %! x = [5:5:50]'/100;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
131 %! gamma = 0.5772156649;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
132 %! y_exp = [0.9876375971;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
133 %! 0.9755453033;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
134 %! 0.9637156702;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
135 %! 0.9521414833;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
136 %! 0.9408157528;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
137 %! 0.9297317075;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
138 %! 0.9188827858;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
139 %! 0.9082626297;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
140 %! 0.8978650778;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
141 %! 0.8876841584 ];
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
142 %! y = (expint (x) + log(x) + gamma) ./ x;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
143 %! assert (y, y_exp, 1e-9);
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
144 %!test
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
145 %! x = [50:5:95]'/100;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
146 %! y_exp = [0.559773595;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
147 %! 0.503364081;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
148 %! 0.454379503;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
149 %! 0.411516976;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
150 %! 0.373768843;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
151 %! 0.340340813;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
152 %! 0.310596579;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
153 %! 0.284019269;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
154 %! 0.260183939;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
155 %! 0.238737524 ];
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
156 %! y = expint (x);
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
157 %! assert (y, y_exp, 1e-9);
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
158 %!test
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
159 %! x = [100:5:145]'/100;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
160 %! y_exp = [0.219383934;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
161 %! 0.201872813;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
162 %! 0.185990905;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
163 %! 0.171555354;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
164 %! 0.158408437;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
165 %! 0.146413373;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
166 %! 0.135450958;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
167 %! 0.125416844;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
168 %! 0.116219313;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
169 %! 0.107777440 ];
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
170 %! y = expint (x);
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
171 %! assert (y, y_exp, 1e-9);
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
172 %!test
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
173 %! x = [150:5:200]'/100;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
174 %! y_exp = [0.100019582;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
175 %! 0.092882108;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
176 %! 0.086308334;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
177 %! 0.080247627;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
178 %! 0.074654644;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
179 %! 0.069488685;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
180 %! 0.064713129;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
181 %! 0.060294967;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
182 %! 0.056204378;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
183 %! 0.052414380;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
184 %! 0.048900511 ];
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
185 %! y = expint (x);
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
186 %! assert (y, y_exp, 1e-9);
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
187
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
188 %% Test input validation
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
189 %!error expint ()
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
190 %!error expint (1,2)